Multiple Hill Republicans on Monday called for congressional action to alter or end the practice.

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June 18, 2018, 7:28 PM GMT / Updated June 18, 2018, 11:24 PM GMT

By Rebecca Shabad and Alex Moe

WASHINGTON — A growing number of GOP lawmakers on Monday expressed outrage at President Donald Trump’s “zero-tolerance” policy of separating migrant children from their parents at the U.S.-Mexico border, with many calling for its reversal through legislation.

Rep. Mario Diaz-Balart, R-Fla., a supporter of an effort by moderate Republicans to force immigration floor votes, tweeted that the policy “must stop” and will work with his colleagues to ensure that a provision addressing the issue is included in immigration legislation that the House is set to vote on this week.

“It is totally unacceptable, for any reason, to purposely separate minor children from their parents," Diaz-Balart said. "Any and every other option should be implemented in order to not separate minors from their parents, which I believe is unconscionable."

Two GOP leadership sources confirmed to NBC News on Monday that votes on two House immigration bills — the conservative Goodlatte bill and the compromise immigration bill — will likely take place on Thursday, with another senior House Republican source saying family separation at the border will be addressed in both bills.

The drafts of both bills, which have not yet been filed, will "ensur[e] accompanied alien minors apprehended at the border can remain with their parent or legal guardian while in DHS custody," said the source, who added that drafters are also working to include a provision that deals with DOJ custody as well.

Speaker Paul Ryan, R-Wis., said on WISN radio Monday morning that Senate Majority Leader Mitch McConnell, R-Ky., has led him to believe that the upper chamber could pass the compromise bill if it passes the House.

In the meantime, several Hill Republicans were harshly critical of the policy, urging congressional action to end it. “It is time for this ugly and inhumane practice to end. Now,” said Rep. Fred Upton, R-Mich., in a statement. “It’s never acceptable to use kids as bargaining chips in political process. For some time, I’ve said that separating young, innocent children from their parents is the wrong approach. The right approach is legislation to address the root issues.”

Sen. Marco Rubio, R-Fla., tweeted Monday that Congress should change the law so that families can be kept together at detention facilities.

“Currently govt must either release parents & continue incentive for illegal entry with children or seperate [sic] families by detaining parents. Neither is good. Lets change the law to allow families to be held together at family facilities & shorten detention with expedited hearings,” he tweeted.

And even though the administration has said the family separation policy should be addressed through comprehensive immigration legislation that includes funding for security measures, other Republicans offered standalone proposals to address the issue.

In a lengthy Facebook post, Sen. Ben Sasse, R-Neb., a frequent critic of Trump, said that he’s working on a possible legislative solution with Sen. James Lankford, R-Okla., but suggested that the president has the power to end the policy unilaterally since his administration instituted it in the first place.

“The president should immediately end this family separation policy," Sasse said. "And he should announce to the Congress the narrowest possible way problems like the FIores consent decree and related decisions (which bias policy toward release into the U.S. within three weeks after capture) can be resolved."

And with a blistering statement Monday evening lashing out at the Trump administration, Sen. Ted Cruz, R-Texas, pledged to introduce his own plan.

“All Americans are rightly horrified by the images we are seeing on the news, children in tears pulled away from their mothers and fathers. This must stop. Now. We can end this crisis by passing the legislation I am introducing this week,” Cruz said.

Cruz said he would be introducing the Protect Kids and Parents Act, emergency legislation that would authorize new temporary shelters with accommodations to keep families together.

“While these cases are pending, families should stay together. Children belong with their mothers and fathers. Once their cases have been adjudicated — under my legislation, in no longer than 14 days — those who meet the legal standard should be granted asylum and those who don’t should be immediately returned to their home country,” he said.

Any GOP Senate supporters of the current family separation policy were mostly quiet Monday, although Sen. Pat Toomey of Pennsylvania did suggest the process should be altered — but not eliminated.

“I don’t think [Attorney General Jeff Sessions] should reverse the fundamental policy, but there are some things we ought to look at doing differently, I think,” he said in an interview with radio host Hugh Hewitt, adding that "I think the instance of the, you know, the heart-wrenching separation of a small child from the mother is, has been, the frequency’s been exaggerated significantly.”

All 49 Democrats in the Senate support a bill authored by Sen. Dianne Feinstein of California to reverse the president’s family separation policy.

Rep. Mike Coffman, R-Colo., said in a statement Monday that he had reached out to Feinstein's office to work with her to put a stop "to this human rights disaster."

"Tearing children from the arms of parents and then isolating them alone is antithetical to the America I grew up in, and to the America that I have many times fought to defend," Coffman said. "This isn’t who we are. My colleagues should mark their words and this moment — history won’t remember well those who support the continuation of this policy."

Trump is slated to meet with House Republicans behind closed doors on Capitol Hill on Tuesday evening to discuss immigration policy. The president said Monday that the U.S. “will not be a migrant camp ... not on my watch.” On Friday, he created confusion for hours after saying that he wouldn’t sign the compromise immigration bill even though it includes all of the items he’s demanded. By the end of the day, White House officials said that Trump had misspoke and that he does support the bill.

"I think they’ve got a short porch to solve this politically," said Republican strategist Rick Wilson. "I think it’s a matter of days, not weeks."

He predicted Trump would soon shift course. "He will abandon them before he will take a public relations hit in my view," Wilson said. "Then he’s going to pat himself on the back and say, 'I was the one who helped these suffering children.'"